Equivocation is the fallacy that occurs when the meaning of an ambiguous term is covertly switched during the reasoning. An ambiguous term is used with one meaning at the beginning of the argument, but then used with a different meaning later in the argument. Because many words have more than one literal meaning, there are many opportunities of this fallacy to occur.

A feather is light.
What is light cannot be dark.
Therefore, a feather cannot be dark.

Two distinct meanings of the word “light” are used in the same argument. In the premise, the word “light” is used to mean “not heavy” and in the middle term “light” is used in its optical sense. Because the two definitions are unrelated, the premise does not bear on the conclusion, even though the same word is used throughout.

Equivocation is often used to form jokes, such as in Mae Wests’s quip: “Marriage is a fine institution, but I'm not ready for an institution”, or Henny Youngman’s standard: “Take my wife … please”. Equivocation is more harmful and consequential when it is used to advance a false conclusion, for example, you may hear the argument:

"Because it's called the theory of evolution, evolution is no more than an unproven assumption!"[2]

Dismissing evolution as “only a theory” is a fallacy based on an incorrect definition of the word "theory".

This is fallacious because it equivocates two different meanings of the word "theory." In the first use, “theory” refers to a scientific theory which is a well-substantiated explanation of some aspect of the natural world that is acquired through the scientific method and repeatedly tested and confirmed through observation and experimentation. In the second use “theory” refers to a tentative idea formed by speculation.

A similar fallacy is evident in this example:

"You have faith in science, and I have faith in God."

This fallacy exploits the fact that "faith" is often used to mean "confidence," that is having a solid reason to be confident of something due to its past performance—this argument is an effort to equate science with religion, when in reality science does not require faith (meaning strong belief, based on spiritual apprehension rather than proof.).[3]

The fallacy of Amphiboly occurs when a syntactic ambiguity allows one meaning to be used in the premise and another meaning to be used in the conclusion.

This fallacy is similar to equivocation but exploits an ambiguous grammatical construct rather than an ambiguous word. A sign stating “No Smoking Permitted” can be interpreted to mean that it is permissible to not smoke, but it is also permissible to smoke, since smoking is not specifically prohibited by the ambiguous language. As with equivocation, amphiboly can be used to create jokes, such as the Groucho Marx quip: "I shot an elephant in my pajamas. How he got into my pajamas I don't know."

Ambiguous language is especially consequential when it appears in policy documents, legal documents, contracts, or constitutions. For example:

No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a grand jury, except in cases arising in the land or naval forces, or in the militia, when in actual service in time of war or public danger…

It is not clear whether the expression "when in actual service in time of war or public danger" attaches just to "in the militia" or to all of "in the land or naval forces, or in the militia". This unclarity makes a big difference, especially to someone "in the land or naval forces" who has been accused of committing a crime during peacetime.[4]

The fallacy of accent (also referred to as accentus, or misleading accent) is a type of ambiguity that arises when the meaning of a sentence is changed by placing an unusual verbal emphasis or when, in a written passage, it is left unclear on which word the emphasis was supposed to fall.

Consider the various meanings a change in emphasis causes in this simple example:

I didn't take the test yesterday. (Somebody else did.)
I didn't take the test yesterday. (I did not take it.)
I didn't take the test yesterday. (I did something else with it.)
I didn't take the test yesterday. (I took a different one.)
I didn't take the test yesterday. (I took something else.)
I didn't take the test yesterday. (I took it some other day.)

When a premise relies for its apparent meaning on one possible emphasis, but a conclusion is drawn that relies on the meaning of the same words accented differently, the fallacy of accent is committed.[5]

Consider the sentence: "I resent that letter." This could mean either that one sent the letter again, or that one has a feeling of resentment towards it. If you concluded, falsely, on the basis of the sentence, that the speaker sent the letter again, then you would have committed a fallacy of accent.[6]

Construing the fallacy more broadly, it can include distortions caused by pulling a quoted passage out of context.[7] This is often done maliciously in politics, for example:

In the 2000 United States Republican primary campaign, George W. Bush's campaign screened advertising including a "warning" from John McCain's "conservative hometown paper" that "It's time the rest of the nation learns about the McCain we know."

The paper (The Arizona Republic), however, went on to say, "There is much there to admire. After all, we have supported McCain in his past runs for office."[8]

The fallacy of composition arises when a conclusion is drawn about a whole based on the features of its constituent elements when, in fact, no justification is provided for the inference. There are actually two types of this fallacy, both of which are known by the same name (because of the high degree of similarity).

The first type of fallacy of Composition arises when a person reasons from the characteristics of individual members of a class or group to a conclusion regarding the characteristics of the entire class or group (taken as a whole). More formally, the "reasoning" would look something like this.[9]

Consider this example: “Every player on the team is a superstar and a great player, so the team is a great team." This is fallacious since the superstars might not be able to play together very well and hence they could be a lousy team. It is also a fallacy to argue if someone stands up out of their seat at a cricket match, they can see better. Therefore, if everyone stands up, they can all see better.

The second type of fallacy of Composition is committed when it is concluded that what is true of the parts of a whole must be true of the whole without there being adequate justification for the claim. More formally, the line of “reasoning" would be as follows:[10]

All of the parts of the object O have the property P.
Therefore, O has the property P.
(Where the property P is one which does not distribute from parts to a whole.)

This sort of reasoning is fallacious because it cannot be inferred that simply because the parts of a complex whole have (or lack) certain properties that the whole that they are parts of has those properties. This is especially clear in math: The numbers 1 and 3 are both odd. 1 and 3 are parts of 4. However it is invalid to conclude the number 4 is odd.

Here are more examples of the fallacy:

The human body is made up of cells, which are invisible. Therefore, the body is invisible.

Both sodium and chlorine are to harmful humans, therefore any combination of sodium and chlorine, for example table salt, will be dangerous to humans.[11]

Arguing that because each individual can profit by consuming a larger share of a common shared resource such as fish from the sea, it is good for all to consume larger shares leads to the tragedy of the commons.